宝くじが当たると思いますか？組合せ論入門

In this class we will explore the basics of calculating combinations and permutations and make connections to calculating the odds of winning the lottery, cracking codes, etc. 

We will: 
Discuss the purpose of counting formulas using some common scenarios;
Explore the differences between combinations and permutations;
Derive the formulas for calculating combinations and permutations.

Then we will apply these concepts to some common interesting problems such as: 
What is the likelihood that you can guess your friend's locker combination? 
What are the chances that a monkey with a typewriter could randomly write a given sentence? 
. . . and of course . . . 
What are your chances of winning the lottery? 
 

Week 1
Permutations: We will explore Permutations, derive the formulas, and discuss how to know when each of the permutation formulas should be used. We will then practice with a variety of problems. 

Week 2
Combinations: We will explore Combinations, derive the formulas, and discuss how to know when each of the combination formulas should be used. We will then practice with a variety of problems. 

Week 3
Putting it all together! In this session we will explore a variety of combination and permutation problems and see how this knowledge can help to answer the question of, "What are my chances of winning the lottery?" and other mathematical probabilities.